pacman::p_load(olsrr, ggstatsplot, ggpubr, sf, spdep, GWmodel, tmap, tidyverse, gtsummary, performance, see, sfdep)In-class Ex 7
1. Overview
2. Importing & Transforming Data
mpsz <- st_read(dsn = "data/geospatial", layer = "MP14_SUBZONE_WEB_PL") %>%
st_transform(3414)Reading layer `MP14_SUBZONE_WEB_PL' from data source
`/Users/stephentay/stephentay/ISSS626-Geospatial-Analytics/In-class_Ex/In-class_Ex07/data/geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 323 features and 15 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21Since there are lat/long in the csv file and you do not know the coordinate system, you make a best guess and indicate the closest geographical coordinate system (which is 4326 in this case). You can double confirm whether 4326 is the correct one by plotting it and check whether it matches the real world. We then transform it to projected coordinate system (3414).
condo_resale = read_csv("data/aspatial/Condo_resale_2015.csv")
head(condo_resale)# A tibble: 6 × 23
LATITUDE LONGITUDE POSTCODE SELLING_PRICE AREA_SQM AGE PROX_CBD
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 1.29 104. 118635 3000000 309 30 7.94
2 1.33 104. 288420 3880000 290 32 6.61
3 1.31 104. 267833 3325000 248 33 6.90
4 1.31 104. 258380 4250000 127 7 4.04
5 1.32 104. 467169 1400000 145 28 11.8
6 1.31 104. 466472 1320000 139 22 10.3
# ℹ 16 more variables: PROX_CHILDCARE <dbl>, PROX_ELDERLYCARE <dbl>,
# PROX_URA_GROWTH_AREA <dbl>, PROX_HAWKER_MARKET <dbl>,
# PROX_KINDERGARTEN <dbl>, PROX_MRT <dbl>, PROX_PARK <dbl>,
# PROX_PRIMARY_SCH <dbl>, PROX_TOP_PRIMARY_SCH <dbl>,
# PROX_SHOPPING_MALL <dbl>, PROX_SUPERMARKET <dbl>, PROX_BUS_STOP <dbl>,
# NO_Of_UNITS <dbl>, FAMILY_FRIENDLY <dbl>, FREEHOLD <dbl>,
# LEASEHOLD_99YR <dbl>condo_resale_sf = condo_resale %>%
st_as_sf(coords = c("LONGITUDE", "LATITUDE"),
crs=4326) %>% # use the geo coordinate system of the lat/long in the csv file
st_transform(crs=3414)
head(condo_resale_sf)Simple feature collection with 6 features and 21 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 22085.12 ymin: 29951.54 xmax: 41042.56 ymax: 34546.2
Projected CRS: SVY21 / Singapore TM
# A tibble: 6 × 22
POSTCODE SELLING_PRICE AREA_SQM AGE PROX_CBD PROX_CHILDCARE PROX_ELDERLYCARE
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 118635 3000000 309 30 7.94 0.166 2.52
2 288420 3880000 290 32 6.61 0.280 1.93
3 267833 3325000 248 33 6.90 0.429 0.502
4 258380 4250000 127 7 4.04 0.395 1.99
5 467169 1400000 145 28 11.8 0.119 1.12
6 466472 1320000 139 22 10.3 0.125 0.789
# ℹ 15 more variables: PROX_URA_GROWTH_AREA <dbl>, PROX_HAWKER_MARKET <dbl>,
# PROX_KINDERGARTEN <dbl>, PROX_MRT <dbl>, PROX_PARK <dbl>,
# PROX_PRIMARY_SCH <dbl>, PROX_TOP_PRIMARY_SCH <dbl>,
# PROX_SHOPPING_MALL <dbl>, PROX_SUPERMARKET <dbl>, PROX_BUS_STOP <dbl>,
# NO_Of_UNITS <dbl>, FAMILY_FRIENDLY <dbl>, FREEHOLD <dbl>,
# LEASEHOLD_99YR <dbl>, geometry <POINT [m]>3. Building the Hedonic Price Model
Correlation Matrix
To avoid multicollinearity, it’s always important to check the relationship between variables to identify any variables with high correlation.
ggcorrmat(condo_resale[, 5:23])
Initial MLR Model
condo_mlr <- lm(formula = SELLING_PRICE ~ AREA_SQM + AGE +
PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE +
PROX_URA_GROWTH_AREA + PROX_HAWKER_MARKET + PROX_KINDERGARTEN +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH +
PROX_TOP_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_SUPERMARKET +
PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD +
LEASEHOLD_99YR,
data=condo_resale_sf)
summary(condo_mlr)
Call:
lm(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD + PROX_CHILDCARE +
PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA + PROX_HAWKER_MARKET +
PROX_KINDERGARTEN + PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH +
PROX_TOP_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_SUPERMARKET +
PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD +
LEASEHOLD_99YR, data = condo_resale_sf)
Residuals:
Min 1Q Median 3Q Max
-3471036 -286903 -22426 239412 12254549
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 543071.4 136210.9 3.987 7.03e-05 ***
AREA_SQM 12688.7 370.1 34.283 < 2e-16 ***
AGE -24566.0 2766.0 -8.881 < 2e-16 ***
PROX_CBD -78122.0 6791.4 -11.503 < 2e-16 ***
PROX_CHILDCARE -333219.0 111020.3 -3.001 0.002734 **
PROX_ELDERLYCARE 170950.0 42110.8 4.060 5.19e-05 ***
PROX_URA_GROWTH_AREA 38507.6 12523.7 3.075 0.002147 **
PROX_HAWKER_MARKET 23801.2 29299.9 0.812 0.416739
PROX_KINDERGARTEN 144098.0 82738.7 1.742 0.081795 .
PROX_MRT -322775.9 58528.1 -5.515 4.14e-08 ***
PROX_PARK 564487.9 66563.0 8.481 < 2e-16 ***
PROX_PRIMARY_SCH 186170.5 65515.2 2.842 0.004553 **
PROX_TOP_PRIMARY_SCH -477.1 20598.0 -0.023 0.981525
PROX_SHOPPING_MALL -207721.5 42855.5 -4.847 1.39e-06 ***
PROX_SUPERMARKET -48074.7 77145.3 -0.623 0.533273
PROX_BUS_STOP 675755.0 138552.0 4.877 1.20e-06 ***
NO_Of_UNITS -216.2 90.3 -2.394 0.016797 *
FAMILY_FRIENDLY 142128.3 47055.1 3.020 0.002569 **
FREEHOLD 300646.5 77296.5 3.890 0.000105 ***
LEASEHOLD_99YR -77137.4 77570.9 -0.994 0.320192
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 755800 on 1416 degrees of freedom
Multiple R-squared: 0.652, Adjusted R-squared: 0.6474
F-statistic: 139.6 on 19 and 1416 DF, p-value: < 2.2e-16Model Assessment Report (using olsrr)
In model assessment, we first check the p-value of the model and the R2. Then after that, we will look at individual variables to check whether any of them which are non-statistically significant which should be eliminated from the model.
ols_regress(condo_mlr) Model Summary
-----------------------------------------------------------------------------
R 0.807 RMSE 750537.537
R-Squared 0.652 MSE 571262902261.220
Adj. R-Squared 0.647 Coef. Var 43.160
Pred R-Squared 0.637 AIC 42971.173
MAE 412117.987 SBC 43081.835
-----------------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
--------------------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
--------------------------------------------------------------------------------
Regression 1.515738e+15 19 7.977571e+13 139.648 0.0000
Residual 8.089083e+14 1416 571262902261.220
Total 2.324647e+15 1435
--------------------------------------------------------------------------------
Parameter Estimates
-----------------------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
-----------------------------------------------------------------------------------------------------------------
(Intercept) 543071.420 136210.918 3.987 0.000 275874.535 810268.305
AREA_SQM 12688.669 370.119 0.579 34.283 0.000 11962.627 13414.710
AGE -24566.001 2766.041 -0.166 -8.881 0.000 -29991.980 -19140.022
PROX_CBD -78121.985 6791.377 -0.267 -11.503 0.000 -91444.227 -64799.744
PROX_CHILDCARE -333219.036 111020.303 -0.087 -3.001 0.003 -551000.984 -115437.089
PROX_ELDERLYCARE 170949.961 42110.748 0.083 4.060 0.000 88343.803 253556.120
PROX_URA_GROWTH_AREA 38507.622 12523.661 0.059 3.075 0.002 13940.700 63074.545
PROX_HAWKER_MARKET 23801.197 29299.923 0.019 0.812 0.417 -33674.725 81277.120
PROX_KINDERGARTEN 144097.972 82738.669 0.030 1.742 0.082 -18205.570 306401.514
PROX_MRT -322775.874 58528.079 -0.123 -5.515 0.000 -437586.937 -207964.811
PROX_PARK 564487.876 66563.011 0.148 8.481 0.000 433915.162 695060.590
PROX_PRIMARY_SCH 186170.524 65515.193 0.072 2.842 0.005 57653.253 314687.795
PROX_TOP_PRIMARY_SCH -477.073 20597.972 -0.001 -0.023 0.982 -40882.894 39928.747
PROX_SHOPPING_MALL -207721.520 42855.500 -0.109 -4.847 0.000 -291788.613 -123654.427
PROX_SUPERMARKET -48074.679 77145.257 -0.012 -0.623 0.533 -199405.956 103256.599
PROX_BUS_STOP 675755.044 138551.991 0.133 4.877 0.000 403965.817 947544.272
NO_Of_UNITS -216.180 90.302 -0.046 -2.394 0.017 -393.320 -39.040
FAMILY_FRIENDLY 142128.272 47055.082 0.056 3.020 0.003 49823.107 234433.438
FREEHOLD 300646.543 77296.529 0.117 3.890 0.000 149018.525 452274.561
LEASEHOLD_99YR -77137.375 77570.869 -0.030 -0.994 0.320 -229303.551 75028.801
-----------------------------------------------------------------------------------------------------------------Multicollinearity
We look at the VIF to check for any variables resulting in multi-collinearity (monitor the model/variables if VIF is between 5-10, and eliminate if VIF is above 10). Since all the variables are less than 10, we do not need to eliminate any of the variables.
ols_vif_tol(condo_mlr) Variables Tolerance VIF
1 AREA_SQM 0.8601326 1.162611
2 AGE 0.7011585 1.426211
3 PROX_CBD 0.4575471 2.185567
4 PROX_CHILDCARE 0.2898233 3.450378
5 PROX_ELDERLYCARE 0.5922238 1.688551
6 PROX_URA_GROWTH_AREA 0.6614081 1.511926
7 PROX_HAWKER_MARKET 0.4373874 2.286303
8 PROX_KINDERGARTEN 0.8356793 1.196631
9 PROX_MRT 0.4949877 2.020252
10 PROX_PARK 0.8015728 1.247547
11 PROX_PRIMARY_SCH 0.3823248 2.615577
12 PROX_TOP_PRIMARY_SCH 0.4878620 2.049760
13 PROX_SHOPPING_MALL 0.4903052 2.039546
14 PROX_SUPERMARKET 0.6142127 1.628100
15 PROX_BUS_STOP 0.3311024 3.020213
16 NO_Of_UNITS 0.6543336 1.528272
17 FAMILY_FRIENDLY 0.7191719 1.390488
18 FREEHOLD 0.2728521 3.664990
19 LEASEHOLD_99YR 0.2645988 3.779307Variable Selection
Using stepwise forward selection method. It’s important that we use the p-value as the selection criteria as we want all our variables to be signficant.
condo_fw_mlr <- ols_step_forward_p(condo_mlr,
p_val = 0.05,
details = FALSE)plot(condo_fw_mlr)
Test for Non-linearity
ols_plot_resid_fit(condo_fw_mlr$model)
Test of Normality of Residuals
ols_plot_resid_hist(condo_fw_mlr$model)
ols_test_normality(condo_fw_mlr$model)-----------------------------------------------
Test Statistic pvalue
-----------------------------------------------
Shapiro-Wilk 0.6856 0.0000
Kolmogorov-Smirnov 0.1366 0.0000
Cramer-von Mises 121.0768 0.0000
Anderson-Darling 67.9551 0.0000
-----------------------------------------------Test for Spatial Autocorrelation
The hedonic model we try to build are using geographically referenced attributes, hence it is also important for us to visual the residual of the hedonic pricing model. In order to perform spatial autocorrelation test, we need to convert condo resale sf from sf data frame into a SpatialPointsDataFrame. First, we will export the residual of the hedonic pricing model and save it as a data frame.
mlr_output <- as.data.frame(condo_fw_mlr$model$residuals) %>%
rename(`FW_MLR_RES` = `condo_fw_mlr$model$residuals`)Next, we will join the newly created dataframe with condo_resale_sf object.
condo_resale_sf <- cbind(condo_resale_sf,
mlr_output$FW_MLR_RES) %>%
rename(`MLR_RES` = `mlr_output.FW_MLR_RES`)Plotting of Residuals
We plot the residuals to see which are over-estimated and which are under-estimated. Since visually there are clusters of over-estimated and under-estimated prices, then this could be signs of spatial auto-correlation.
tmap_mode("view")
#tmap_options(check.and.fix = TRUE) -- add this code here to fix any layers with problematic lines/polygons.
tm_shape(mpsz) +
tmap_options(check.and.fix = TRUE) + # add this line here to explicitly fix problematic polygons in this specific layer.
tm_polygons(alpha = 0.4) +
tm_shape(condo_resale_sf) +
tm_dots(col = "MLR_RES",
alpha = 0.6,
style="quantile") +
tm_view(set.zoom.limits = c(11,14))tmap_mode("plot")condo_resale_sf <- condo_resale_sf %>%
mutate(nb = st_knn(geometry, k = 6, longlat = FALSE),
wt = st_weights(nb, style = "W"),
.before = 1)We run global moran i permuatation test to check whether there are spatial autocorrelation of the prices. The Global Moran’s I test for residual spatial autocorrelation shows that it’s p-value is less than the alpha value of 0.05. Hence, we will reject the null hypothesis that the residuals are randomly distributed. Since the Observed Global Moran I = 0.25586 which is greater than 0, we can infer than the residuals resemble cluster distribution.
global_moran_perm(condo_resale_sf$MLR_RES,
condo_resale_sf$nb,
condo_resale_sf$wt,
alternative = "two.sided",
nsim = 99)
Monte-Carlo simulation of Moran I
data: x
weights: listw
number of simulations + 1: 100
statistic = 0.32254, observed rank = 100, p-value < 2.2e-16
alternative hypothesis: two.sided4. Build Fixed Bandwidth GWR Model
bw_fixed <- bw.gwr(formula = SELLING_PRICE ~ AREA_SQM + AGE +
PROX_CBD + PROX_CHILDCARE +
PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH +
PROX_SHOPPING_MALL + PROX_BUS_STOP +
NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale_sf,
approach="CV",
kernel = "gaussian",
adaptive = FALSE,
longlat = FALSE)Fixed bandwidth: 17660.96 CV score: 8.259118e+14
Fixed bandwidth: 10917.26 CV score: 7.970454e+14
Fixed bandwidth: 6749.419 CV score: 7.273273e+14
Fixed bandwidth: 4173.553 CV score: 6.300006e+14
Fixed bandwidth: 2581.58 CV score: 5.404958e+14
Fixed bandwidth: 1597.687 CV score: 4.857515e+14
Fixed bandwidth: 989.6077 CV score: 4.722431e+14
Fixed bandwidth: 613.7939 CV score: 1.379526e+16
Fixed bandwidth: 1221.873 CV score: 4.778717e+14
Fixed bandwidth: 846.0596 CV score: 4.791629e+14
Fixed bandwidth: 1078.325 CV score: 4.751406e+14
Fixed bandwidth: 934.7772 CV score: 4.72518e+14
Fixed bandwidth: 1023.495 CV score: 4.730305e+14
Fixed bandwidth: 968.6643 CV score: 4.721317e+14
Fixed bandwidth: 955.7206 CV score: 4.722072e+14
Fixed bandwidth: 976.6639 CV score: 4.721387e+14
Fixed bandwidth: 963.7202 CV score: 4.721484e+14
Fixed bandwidth: 971.7199 CV score: 4.721293e+14
Fixed bandwidth: 973.6083 CV score: 4.721309e+14
Fixed bandwidth: 970.5527 CV score: 4.721295e+14
Fixed bandwidth: 972.4412 CV score: 4.721296e+14
Fixed bandwidth: 971.2741 CV score: 4.721292e+14
Fixed bandwidth: 970.9985 CV score: 4.721293e+14
Fixed bandwidth: 971.4443 CV score: 4.721292e+14
Fixed bandwidth: 971.5496 CV score: 4.721293e+14
Fixed bandwidth: 971.3793 CV score: 4.721292e+14
Fixed bandwidth: 971.3391 CV score: 4.721292e+14
Fixed bandwidth: 971.3143 CV score: 4.721292e+14
Fixed bandwidth: 971.3545 CV score: 4.721292e+14
Fixed bandwidth: 971.3296 CV score: 4.721292e+14
Fixed bandwidth: 971.345 CV score: 4.721292e+14
Fixed bandwidth: 971.3355 CV score: 4.721292e+14
Fixed bandwidth: 971.3413 CV score: 4.721292e+14
Fixed bandwidth: 971.3377 CV score: 4.721292e+14
Fixed bandwidth: 971.34 CV score: 4.721292e+14
Fixed bandwidth: 971.3405 CV score: 4.721292e+14
Fixed bandwidth: 971.3396 CV score: 4.721292e+14
Fixed bandwidth: 971.3402 CV score: 4.721292e+14
Fixed bandwidth: 971.3398 CV score: 4.721292e+14
Fixed bandwidth: 971.34 CV score: 4.721292e+14
Fixed bandwidth: 971.3399 CV score: 4.721292e+14
Fixed bandwidth: 971.34 CV score: 4.721292e+14 You can see the improvements in R2 and the AICc. AICc is robust for small dataset.
gwr_fixed <- gwr.basic(formula = SELLING_PRICE ~ AREA_SQM + AGE +
PROX_CBD + PROX_CHILDCARE +
PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH +
PROX_SHOPPING_MALL + PROX_BUS_STOP +
NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale_sf,
bw=bw_fixed,
kernel = 'gaussian',
longlat = FALSE)
gwr_fixed ***********************************************************************
* Package GWmodel *
***********************************************************************
Program starts at: 2024-10-14 22:21:23.142639
Call:
gwr.basic(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD +
PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + PROX_SHOPPING_MALL +
PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data = condo_resale_sf, bw = bw_fixed, kernel = "gaussian",
longlat = FALSE)
Dependent (y) variable: SELLING_PRICE
Independent variables: AREA_SQM AGE PROX_CBD PROX_CHILDCARE PROX_ELDERLYCARE PROX_URA_GROWTH_AREA PROX_MRT PROX_PARK PROX_PRIMARY_SCH PROX_SHOPPING_MALL PROX_BUS_STOP NO_Of_UNITS FAMILY_FRIENDLY FREEHOLD
Number of data points: 1436
***********************************************************************
* Results of Global Regression *
***********************************************************************
Call:
lm(formula = formula, data = data)
Residuals:
Min 1Q Median 3Q Max
-3470778 -298119 -23481 248917 12234210
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 527633.22 108183.22 4.877 1.20e-06 ***
AREA_SQM 12777.52 367.48 34.771 < 2e-16 ***
AGE -24687.74 2754.84 -8.962 < 2e-16 ***
PROX_CBD -77131.32 5763.12 -13.384 < 2e-16 ***
PROX_CHILDCARE -318472.75 107959.51 -2.950 0.003231 **
PROX_ELDERLYCARE 185575.62 39901.86 4.651 3.61e-06 ***
PROX_URA_GROWTH_AREA 39163.25 11754.83 3.332 0.000885 ***
PROX_MRT -294745.11 56916.37 -5.179 2.56e-07 ***
PROX_PARK 570504.81 65507.03 8.709 < 2e-16 ***
PROX_PRIMARY_SCH 159856.14 60234.60 2.654 0.008046 **
PROX_SHOPPING_MALL -220947.25 36561.83 -6.043 1.93e-09 ***
PROX_BUS_STOP 682482.22 134513.24 5.074 4.42e-07 ***
NO_Of_UNITS -245.48 87.95 -2.791 0.005321 **
FAMILY_FRIENDLY 146307.58 46893.02 3.120 0.001845 **
FREEHOLD 350599.81 48506.48 7.228 7.98e-13 ***
---Significance stars
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 756000 on 1421 degrees of freedom
Multiple R-squared: 0.6507
Adjusted R-squared: 0.6472
F-statistic: 189.1 on 14 and 1421 DF, p-value: < 2.2e-16
***Extra Diagnostic information
Residual sum of squares: 8.120609e+14
Sigma(hat): 752522.9
AIC: 42966.76
AICc: 42967.14
BIC: 41731.39
***********************************************************************
* Results of Geographically Weighted Regression *
***********************************************************************
*********************Model calibration information*********************
Kernel function: gaussian
Fixed bandwidth: 971.34
Regression points: the same locations as observations are used.
Distance metric: Euclidean distance metric is used.
****************Summary of GWR coefficient estimates:******************
Min. 1st Qu. Median 3rd Qu.
Intercept -3.5988e+07 -5.1998e+05 7.6780e+05 1.7412e+06
AREA_SQM 1.0003e+03 5.2758e+03 7.4740e+03 1.2301e+04
AGE -1.3475e+05 -2.0813e+04 -8.6260e+03 -3.7784e+03
PROX_CBD -7.7047e+07 -2.3608e+05 -8.3599e+04 3.4646e+04
PROX_CHILDCARE -6.0097e+06 -3.3667e+05 -9.7426e+04 2.9007e+05
PROX_ELDERLYCARE -3.5001e+06 -1.5970e+05 3.1970e+04 1.9577e+05
PROX_URA_GROWTH_AREA -3.0170e+06 -8.2013e+04 7.0749e+04 2.2612e+05
PROX_MRT -3.5282e+06 -6.5836e+05 -1.8833e+05 3.6922e+04
PROX_PARK -1.2062e+06 -2.1732e+05 3.5383e+04 4.1335e+05
PROX_PRIMARY_SCH -2.2695e+07 -1.7066e+05 4.8472e+04 5.1555e+05
PROX_SHOPPING_MALL -7.2585e+06 -1.6684e+05 -1.0517e+04 1.5923e+05
PROX_BUS_STOP -1.4676e+06 -4.5207e+04 3.7601e+05 1.1664e+06
NO_Of_UNITS -1.3170e+03 -2.4822e+02 -3.0846e+01 2.5496e+02
FAMILY_FRIENDLY -2.2749e+06 -1.1140e+05 7.6214e+03 1.6107e+05
FREEHOLD -9.2067e+06 3.8074e+04 1.5169e+05 3.7528e+05
Max.
Intercept 112794435
AREA_SQM 21575
AGE 434203
PROX_CBD 2704604
PROX_CHILDCARE 1654086
PROX_ELDERLYCARE 38867861
PROX_URA_GROWTH_AREA 78515805
PROX_MRT 3124325
PROX_PARK 18122439
PROX_PRIMARY_SCH 4637517
PROX_SHOPPING_MALL 1529953
PROX_BUS_STOP 11342209
NO_Of_UNITS 12907
FAMILY_FRIENDLY 1720745
FREEHOLD 6073642
************************Diagnostic information*************************
Number of data points: 1436
Effective number of parameters (2trace(S) - trace(S'S)): 438.3807
Effective degrees of freedom (n-2trace(S) + trace(S'S)): 997.6193
AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 42263.61
AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 41632.36
BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 42515.71
Residual sum of squares: 2.534069e+14
R-square value: 0.8909912
Adjusted R-square value: 0.8430418
***********************************************************************
Program stops at: 2024-10-14 22:21:23.688972 bw_adaptive <- bw.gwr(formula = SELLING_PRICE ~ AREA_SQM + AGE +
PROX_CBD + PROX_CHILDCARE +
PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH +
PROX_SHOPPING_MALL + PROX_BUS_STOP +
NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale_sf,
approach="CV",
kernel = "gaussian",
adaptive = TRUE,
longlat = FALSE)Adaptive bandwidth: 895 CV score: 7.952401e+14
Adaptive bandwidth: 561 CV score: 7.667364e+14
Adaptive bandwidth: 354 CV score: 6.953454e+14
Adaptive bandwidth: 226 CV score: 6.15223e+14
Adaptive bandwidth: 147 CV score: 5.674373e+14
Adaptive bandwidth: 98 CV score: 5.426745e+14
Adaptive bandwidth: 68 CV score: 5.168117e+14
Adaptive bandwidth: 49 CV score: 4.859631e+14
Adaptive bandwidth: 37 CV score: 4.646518e+14
Adaptive bandwidth: 30 CV score: 4.422088e+14
Adaptive bandwidth: 25 CV score: 4.430816e+14
Adaptive bandwidth: 32 CV score: 4.505602e+14
Adaptive bandwidth: 27 CV score: 4.462172e+14
Adaptive bandwidth: 30 CV score: 4.422088e+14 gwr_adaptive <- gwr.basic(formula = SELLING_PRICE ~ AREA_SQM + AGE +
PROX_CBD + PROX_CHILDCARE +
PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH +
PROX_SHOPPING_MALL + PROX_BUS_STOP +
NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale_sf,
bw=bw_adaptive,
kernel = 'gaussian',
adaptive=TRUE,
longlat = FALSE)
gwr_adaptive ***********************************************************************
* Package GWmodel *
***********************************************************************
Program starts at: 2024-10-14 22:21:28.444453
Call:
gwr.basic(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD +
PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + PROX_SHOPPING_MALL +
PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data = condo_resale_sf, bw = bw_adaptive, kernel = "gaussian",
adaptive = TRUE, longlat = FALSE)
Dependent (y) variable: SELLING_PRICE
Independent variables: AREA_SQM AGE PROX_CBD PROX_CHILDCARE PROX_ELDERLYCARE PROX_URA_GROWTH_AREA PROX_MRT PROX_PARK PROX_PRIMARY_SCH PROX_SHOPPING_MALL PROX_BUS_STOP NO_Of_UNITS FAMILY_FRIENDLY FREEHOLD
Number of data points: 1436
***********************************************************************
* Results of Global Regression *
***********************************************************************
Call:
lm(formula = formula, data = data)
Residuals:
Min 1Q Median 3Q Max
-3470778 -298119 -23481 248917 12234210
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 527633.22 108183.22 4.877 1.20e-06 ***
AREA_SQM 12777.52 367.48 34.771 < 2e-16 ***
AGE -24687.74 2754.84 -8.962 < 2e-16 ***
PROX_CBD -77131.32 5763.12 -13.384 < 2e-16 ***
PROX_CHILDCARE -318472.75 107959.51 -2.950 0.003231 **
PROX_ELDERLYCARE 185575.62 39901.86 4.651 3.61e-06 ***
PROX_URA_GROWTH_AREA 39163.25 11754.83 3.332 0.000885 ***
PROX_MRT -294745.11 56916.37 -5.179 2.56e-07 ***
PROX_PARK 570504.81 65507.03 8.709 < 2e-16 ***
PROX_PRIMARY_SCH 159856.14 60234.60 2.654 0.008046 **
PROX_SHOPPING_MALL -220947.25 36561.83 -6.043 1.93e-09 ***
PROX_BUS_STOP 682482.22 134513.24 5.074 4.42e-07 ***
NO_Of_UNITS -245.48 87.95 -2.791 0.005321 **
FAMILY_FRIENDLY 146307.58 46893.02 3.120 0.001845 **
FREEHOLD 350599.81 48506.48 7.228 7.98e-13 ***
---Significance stars
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 756000 on 1421 degrees of freedom
Multiple R-squared: 0.6507
Adjusted R-squared: 0.6472
F-statistic: 189.1 on 14 and 1421 DF, p-value: < 2.2e-16
***Extra Diagnostic information
Residual sum of squares: 8.120609e+14
Sigma(hat): 752522.9
AIC: 42966.76
AICc: 42967.14
BIC: 41731.39
***********************************************************************
* Results of Geographically Weighted Regression *
***********************************************************************
*********************Model calibration information*********************
Kernel function: gaussian
Adaptive bandwidth: 30 (number of nearest neighbours)
Regression points: the same locations as observations are used.
Distance metric: Euclidean distance metric is used.
****************Summary of GWR coefficient estimates:******************
Min. 1st Qu. Median 3rd Qu.
Intercept -1.3487e+08 -2.4669e+05 7.7928e+05 1.6194e+06
AREA_SQM 3.3188e+03 5.6285e+03 7.7825e+03 1.2738e+04
AGE -9.6746e+04 -2.9288e+04 -1.4043e+04 -5.6119e+03
PROX_CBD -2.5330e+06 -1.6256e+05 -7.7242e+04 2.6624e+03
PROX_CHILDCARE -1.2790e+06 -2.0175e+05 8.7158e+03 3.7778e+05
PROX_ELDERLYCARE -1.6212e+06 -9.2050e+04 6.1029e+04 2.8184e+05
PROX_URA_GROWTH_AREA -7.2686e+06 -3.0350e+04 4.5869e+04 2.4613e+05
PROX_MRT -4.3781e+07 -6.7282e+05 -2.2115e+05 -7.4593e+04
PROX_PARK -2.9020e+06 -1.6782e+05 1.1601e+05 4.6572e+05
PROX_PRIMARY_SCH -8.6418e+05 -1.6627e+05 -7.7853e+03 4.3222e+05
PROX_SHOPPING_MALL -1.8272e+06 -1.3175e+05 -1.4049e+04 1.3799e+05
PROX_BUS_STOP -2.0579e+06 -7.1461e+04 4.1104e+05 1.2071e+06
NO_Of_UNITS -2.1993e+03 -2.3685e+02 -3.4699e+01 1.1657e+02
FAMILY_FRIENDLY -5.9879e+05 -5.0927e+04 2.6173e+04 2.2481e+05
FREEHOLD -1.6340e+05 4.0765e+04 1.9023e+05 3.7960e+05
Max.
Intercept 18758355
AREA_SQM 23064
AGE 13303
PROX_CBD 11346650
PROX_CHILDCARE 2892127
PROX_ELDERLYCARE 2465671
PROX_URA_GROWTH_AREA 7384059
PROX_MRT 1186242
PROX_PARK 2588497
PROX_PRIMARY_SCH 3381462
PROX_SHOPPING_MALL 38038564
PROX_BUS_STOP 12081592
NO_Of_UNITS 1010
FAMILY_FRIENDLY 2072414
FREEHOLD 1813995
************************Diagnostic information*************************
Number of data points: 1436
Effective number of parameters (2trace(S) - trace(S'S)): 350.3088
Effective degrees of freedom (n-2trace(S) + trace(S'S)): 1085.691
AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 41982.22
AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 41546.74
BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 41914.08
Residual sum of squares: 2.528227e+14
R-square value: 0.8912425
Adjusted R-square value: 0.8561185
***********************************************************************
Program stops at: 2024-10-14 22:21:29.091162 gwr_adaptive_output <- as.data.frame(gwr_adaptive$SDF) %>%
select(-c(2:15))gwr_sf_adaptive <- cbind(condo_resale_sf,
gwr_adaptive_output)
glimpse(gwr_sf_adaptive)Rows: 1,436
Columns: 63
$ nb <nb> <66, 77, 123, 238, 239, 343>, <21, 162, 163, 19…
$ wt <list> <0.1666667, 0.1666667, 0.1666667, 0.1666667, …
$ POSTCODE <dbl> 118635, 288420, 267833, 258380, 467169, 466472…
$ SELLING_PRICE <dbl> 3000000, 3880000, 3325000, 4250000, 1400000, 1…
$ AREA_SQM <dbl> 309, 290, 248, 127, 145, 139, 218, 141, 165, 1…
$ AGE <dbl> 30, 32, 33, 7, 28, 22, 24, 24, 27, 31, 17, 22,…
$ PROX_CBD <dbl> 7.941259, 6.609797, 6.898000, 4.038861, 11.783…
$ PROX_CHILDCARE <dbl> 0.16597932, 0.28027246, 0.42922669, 0.39473543…
$ PROX_ELDERLYCARE <dbl> 2.5198118, 1.9333338, 0.5021395, 1.9910316, 1.…
$ PROX_URA_GROWTH_AREA <dbl> 6.618741, 7.505109, 6.463887, 4.906512, 6.4106…
$ PROX_HAWKER_MARKET <dbl> 1.76542207, 0.54507614, 0.37789301, 1.68259969…
$ PROX_KINDERGARTEN <dbl> 0.05835552, 0.61592412, 0.14120309, 0.38200076…
$ PROX_MRT <dbl> 0.5607188, 0.6584461, 0.3053433, 0.6910183, 0.…
$ PROX_PARK <dbl> 1.1710446, 0.1992269, 0.2779886, 0.9832843, 0.…
$ PROX_PRIMARY_SCH <dbl> 1.6340256, 0.9747834, 1.4715016, 1.4546324, 0.…
$ PROX_TOP_PRIMARY_SCH <dbl> 3.3273195, 0.9747834, 1.4715016, 2.3006394, 0.…
$ PROX_SHOPPING_MALL <dbl> 2.2102717, 2.9374279, 1.2256850, 0.3525671, 1.…
$ PROX_SUPERMARKET <dbl> 0.9103958, 0.5900617, 0.4135583, 0.4162219, 0.…
$ PROX_BUS_STOP <dbl> 0.10336166, 0.28673408, 0.28504777, 0.29872340…
$ NO_Of_UNITS <dbl> 18, 20, 27, 30, 30, 31, 32, 32, 32, 32, 34, 34…
$ FAMILY_FRIENDLY <dbl> 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0…
$ FREEHOLD <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1…
$ LEASEHOLD_99YR <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ MLR_RES <dbl> -1489099.55, 415494.57, 194129.69, 1088992.71,…
$ Intercept <dbl> 2050011.67, 1633128.24, 3433608.17, 234358.91,…
$ y <dbl> 3000000, 3880000, 3325000, 4250000, 1400000, 1…
$ yhat <dbl> 2886531.8, 3466801.5, 3616527.2, 5435481.6, 13…
$ residual <dbl> 113468.16, 413198.52, -291527.20, -1185481.63,…
$ CV_Score <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ Stud_residual <dbl> 0.38207013, 1.01433140, -0.83780678, -2.846146…
$ Intercept_SE <dbl> 516105.5, 488083.5, 963711.4, 444185.5, 211962…
$ AREA_SQM_SE <dbl> 823.2860, 825.2380, 988.2240, 617.4007, 1376.2…
$ AGE_SE <dbl> 5889.782, 6226.916, 6510.236, 6010.511, 8180.3…
$ PROX_CBD_SE <dbl> 37411.22, 23615.06, 56103.77, 469337.41, 41064…
$ PROX_CHILDCARE_SE <dbl> 319111.1, 299705.3, 349128.5, 304965.2, 698720…
$ PROX_ELDERLYCARE_SE <dbl> 120633.34, 84546.69, 129687.07, 127150.69, 327…
$ PROX_URA_GROWTH_AREA_SE <dbl> 56207.39, 76956.50, 95774.60, 470762.12, 47433…
$ PROX_MRT_SE <dbl> 185181.3, 281133.9, 275483.7, 279877.1, 363830…
$ PROX_PARK_SE <dbl> 205499.6, 229358.7, 314124.3, 227249.4, 364580…
$ PROX_PRIMARY_SCH_SE <dbl> 152400.7, 165150.7, 196662.6, 240878.9, 249087…
$ PROX_SHOPPING_MALL_SE <dbl> 109268.8, 98906.8, 119913.3, 177104.1, 301032.…
$ PROX_BUS_STOP_SE <dbl> 600668.6, 410222.1, 464156.7, 562810.8, 740922…
$ NO_Of_UNITS_SE <dbl> 218.1258, 208.9410, 210.9828, 361.7767, 299.50…
$ FAMILY_FRIENDLY_SE <dbl> 131474.73, 114989.07, 146607.22, 108726.62, 16…
$ FREEHOLD_SE <dbl> 115954.0, 130110.0, 141031.5, 138239.1, 210641…
$ Intercept_TV <dbl> 3.9720784, 3.3460017, 3.5629010, 0.5276150, 1.…
$ AREA_SQM_TV <dbl> 11.614302, 20.087361, 13.247868, 33.577223, 4.…
$ AGE_TV <dbl> -1.6154474, -9.3441881, -4.1023685, -15.524301…
$ PROX_CBD_TV <dbl> -3.22582173, -6.32792021, -4.62353528, 5.17080…
$ PROX_CHILDCARE_TV <dbl> 1.000488185, 1.471786337, -0.344047555, 1.5766…
$ PROX_ELDERLYCARE_TV <dbl> -3.26126929, 3.84626245, 4.13191383, 2.4756745…
$ PROX_URA_GROWTH_AREA_TV <dbl> -2.846248368, -1.848971738, -2.648105057, -5.6…
$ PROX_MRT_TV <dbl> -1.61864578, -8.92998600, -3.40075727, -7.2870…
$ PROX_PARK_TV <dbl> -0.83749312, 2.28192684, 0.66565951, -3.340617…
$ PROX_PRIMARY_SCH_TV <dbl> 1.59230221, 6.70194543, 2.90580089, 12.9836104…
$ PROX_SHOPPING_MALL_TV <dbl> 2.753588422, -0.886626400, -1.056869486, -0.16…
$ PROX_BUS_STOP_TV <dbl> 2.0154464, 4.4941192, 3.0419145, 12.8383775, 0…
$ NO_Of_UNITS_TV <dbl> 0.480589953, -1.380026395, -0.045279967, -0.44…
$ FAMILY_FRIENDLY_TV <dbl> -0.06902748, 2.69655779, 0.04058290, 14.312764…
$ FREEHOLD_TV <dbl> 2.6213469, 3.0452799, 1.1970499, 8.7711485, 1.…
$ Local_R2 <dbl> 0.8846744, 0.8899773, 0.8947007, 0.9073605, 0.…
$ geometry <POINT [m]> POINT (22085.12 29951.54), POINT (25656.…
$ geometry.1 <POINT [m]> POINT (22085.12 29951.54), POINT (25656.…tmap_mode("view")
tm_shape(mpsz)+
tm_polygons(alpha = 0.1) +
tm_shape(gwr_sf_adaptive) +
tm_dots(col = "Local_R2",
border.col = "gray60",
border.lwd = 1) +
tm_view(set.zoom.limits = c(11,14))tmap_mode("plot")bw_adaptivex <- bw.gwr(formula = SELLING_PRICE ~ AREA_SQM + AGE +
PROX_CBD + PROX_CHILDCARE +
PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH +
PROX_SHOPPING_MALL + PROX_BUS_STOP + PROX_TOP_PRIMARY_SCH +
NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale_sf,
approach="CV",
kernel = "gaussian",
adaptive = TRUE,
longlat = FALSE)Adaptive bandwidth: 895 CV score: 7.930182e+14
Adaptive bandwidth: 561 CV score: 7.622347e+14
Adaptive bandwidth: 354 CV score: 6.886542e+14
Adaptive bandwidth: 226 CV score: 6.074912e+14
Adaptive bandwidth: 147 CV score: 5.593322e+14
Adaptive bandwidth: 98 CV score: 5.350358e+14
Adaptive bandwidth: 68 CV score: 5.111188e+14
Adaptive bandwidth: 49 CV score: 4.833426e+14
Adaptive bandwidth: 37 CV score: 4.651988e+14
Adaptive bandwidth: 30 CV score: 4.435755e+14
Adaptive bandwidth: 25 CV score: 4.493824e+14
Adaptive bandwidth: 32 CV score: 4.517619e+14
Adaptive bandwidth: 27 CV score: 4.522979e+14
Adaptive bandwidth: 30 CV score: 4.435755e+14 gwr_adaptivex <- gwr.basic(formula = SELLING_PRICE ~ AREA_SQM + AGE +
PROX_CBD + PROX_CHILDCARE +
PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH +
PROX_SHOPPING_MALL + PROX_BUS_STOP + PROX_TOP_PRIMARY_SCH +
NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale_sf,
bw=bw_adaptivex,
kernel = 'gaussian',
adaptive=TRUE,
longlat = FALSE)
gwr_adaptivex ***********************************************************************
* Package GWmodel *
***********************************************************************
Program starts at: 2024-10-14 22:21:35.015165
Call:
gwr.basic(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD +
PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + PROX_SHOPPING_MALL +
PROX_BUS_STOP + PROX_TOP_PRIMARY_SCH + NO_Of_UNITS + FAMILY_FRIENDLY +
FREEHOLD, data = condo_resale_sf, bw = bw_adaptivex, kernel = "gaussian",
adaptive = TRUE, longlat = FALSE)
Dependent (y) variable: SELLING_PRICE
Independent variables: AREA_SQM AGE PROX_CBD PROX_CHILDCARE PROX_ELDERLYCARE PROX_URA_GROWTH_AREA PROX_MRT PROX_PARK PROX_PRIMARY_SCH PROX_SHOPPING_MALL PROX_BUS_STOP PROX_TOP_PRIMARY_SCH NO_Of_UNITS FAMILY_FRIENDLY FREEHOLD
Number of data points: 1436
***********************************************************************
* Results of Global Regression *
***********************************************************************
Call:
lm(formula = formula, data = data)
Residuals:
Min 1Q Median 3Q Max
-3477028 -295340 -23635 240452 12252600
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 504832.66 111320.09 4.535 6.25e-06 ***
AREA_SQM 12783.55 367.58 34.778 < 2e-16 ***
AGE -24599.37 2756.95 -8.923 < 2e-16 ***
PROX_CBD -78927.31 6122.02 -12.892 < 2e-16 ***
PROX_CHILDCARE -320040.98 107983.78 -2.964 0.003089 **
PROX_ELDERLYCARE 175526.09 41542.82 4.225 2.54e-05 ***
PROX_URA_GROWTH_AREA 41498.48 12058.25 3.442 0.000595 ***
PROX_MRT -295932.67 56937.59 -5.197 2.31e-07 ***
PROX_PARK 568147.60 65568.61 8.665 < 2e-16 ***
PROX_PRIMARY_SCH 153113.91 60735.98 2.521 0.011812 *
PROX_SHOPPING_MALL -208176.02 39400.47 -5.284 1.46e-07 ***
PROX_BUS_STOP 677355.94 134653.66 5.030 5.52e-07 ***
PROX_TOP_PRIMARY_SCH 15518.05 17833.18 0.870 0.384350
NO_Of_UNITS -246.89 87.97 -2.807 0.005075 **
FAMILY_FRIENDLY 145239.62 46913.08 3.096 0.002000 **
FREEHOLD 347136.53 48673.62 7.132 1.57e-12 ***
---Significance stars
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 756000 on 1420 degrees of freedom
Multiple R-squared: 0.6509
Adjusted R-squared: 0.6472
F-statistic: 176.5 on 15 and 1420 DF, p-value: < 2.2e-16
***Extra Diagnostic information
Residual sum of squares: 8.116281e+14
Sigma(hat): 752322.3
AIC: 42967.99
AICc: 42968.42
BIC: 41745.16
***********************************************************************
* Results of Geographically Weighted Regression *
***********************************************************************
*********************Model calibration information*********************
Kernel function: gaussian
Adaptive bandwidth: 30 (number of nearest neighbours)
Regression points: the same locations as observations are used.
Distance metric: Euclidean distance metric is used.
****************Summary of GWR coefficient estimates:******************
Min. 1st Qu. Median 3rd Qu.
Intercept -8.5559e+07 -6.6307e+05 8.5628e+05 1.7386e+06
AREA_SQM 3.3197e+03 5.6395e+03 7.7818e+03 1.2683e+04
AGE -9.6303e+04 -2.9707e+04 -1.3908e+04 -5.8025e+03
PROX_CBD -1.9357e+07 -2.5027e+05 -8.9868e+04 -2.4200e+04
PROX_CHILDCARE -1.2931e+06 -1.7322e+05 1.0810e+03 3.5987e+05
PROX_ELDERLYCARE -2.3281e+06 -5.4486e+04 8.3292e+04 3.1969e+05
PROX_URA_GROWTH_AREA -4.2489e+06 -3.3469e+04 5.8484e+04 3.4738e+05
PROX_MRT -5.4370e+07 -7.4067e+05 -2.1933e+05 -6.7526e+04
PROX_PARK -3.0419e+06 -1.4149e+05 1.5040e+05 5.5204e+05
PROX_PRIMARY_SCH -1.0574e+06 -1.8890e+05 -3.5460e+04 4.9778e+05
PROX_SHOPPING_MALL -1.5702e+06 -1.9888e+05 -2.1442e+04 1.4256e+05
PROX_BUS_STOP -1.7718e+06 -6.0885e+04 4.4049e+05 1.3487e+06
PROX_TOP_PRIMARY_SCH -2.6878e+06 -2.5208e+05 -2.8032e+04 5.1810e+04
NO_Of_UNITS -2.2000e+03 -2.3707e+02 -4.4997e+01 1.1135e+02
FAMILY_FRIENDLY -6.1100e+05 -5.7093e+04 2.2768e+04 2.1691e+05
FREEHOLD -4.1537e+05 4.5485e+04 1.8806e+05 3.6166e+05
Max.
Intercept 24728361
AREA_SQM 23027
AGE 12980
PROX_CBD 7518507
PROX_CHILDCARE 3145612
PROX_ELDERLYCARE 2274410
PROX_URA_GROWTH_AREA 19828744
PROX_MRT 1079051
PROX_PARK 3145150
PROX_PRIMARY_SCH 3313681
PROX_SHOPPING_MALL 46587453
PROX_BUS_STOP 12079040
PROX_TOP_PRIMARY_SCH 11209904
NO_Of_UNITS 1008
FAMILY_FRIENDLY 2053750
FREEHOLD 1817711
************************Diagnostic information*************************
Number of data points: 1436
Effective number of parameters (2trace(S) - trace(S'S)): 359.4269
Effective degrees of freedom (n-2trace(S) + trace(S'S)): 1076.573
AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 41995.92
AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 41542.07
BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 41962.74
Residual sum of squares: 2.505137e+14
R-square value: 0.8922358
Adjusted R-square value: 0.856224
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Program stops at: 2024-10-14 22:21:35.676258